Prunes are very good for constipation but should be an addition to a healthy diet.
I have found both Figs dried/fresh also very good.
I have found a bowl of pruned (say around eight) before my breakfast with the same again in the evening just right for me, if you buy tinned ones look for the ones in Juice rather than Syrup. For figs I would have 3 x twice per day. You can have prune juice which is also good and I would suggest two medium glasses per day.
How quick they will work I cant say exactly, depends on the length of constipation.

How many prunes does it usually take to relieve constipation & how long does that usually take?

How long has it been since you last had a bowel movement ? I eat 6 stewed prunes everyday but it can take up to 24 hours or more for it to work. This doesn't help the stool that is already stored in the rectum from the last 3-4 days. You also have to drink lots of water like 64 oz. a day.
This is what I do when I haven't had a bowel movement in 3-4 days. I use a glycerin suppository to soften the stool that is already in the rectum because that is what will be the hardest to pass. That stool is already dried out and hard and if you try to pass it,you're going to have to push very hard and force it out. Not only will it be very painful but you could cause a small tear just inside the rectum and that will make it even more painful to have bowel movements. Before I even insert the suppository in my rectum, I put a glove on and put a lot of vaseline on my index finger and coat the outside anal area and just inside the rectum with lots of vaseline to help the stool to come out easier and protect my skin from getting sore and irritated. I then put on a clean glove to insert the suppository inside my rectum but I also make sure there is a lot of vaseline on the tip of the suppository to make it easier to insert and to push up as high as you can. After you put the suppository in the then lie on your bed on your left side and pull your left leg up towards your chest as high as possible and stay there until you get a very strong urge to have a bowel movement. This can take as little as 20 minutes to work or as long as an hour. Once you sit on the toilet don't push or force out the stool but take long slow deep breaths and purse your lips and release the air out slowly and keep doing this until you have been able to have a bowel movement. It takes longer this way but it is the pain free way to do it. Take it from someone who has had constipation problems all of her life. The only way I have found to keep from getting constipated all the time is to go on a high fiber diet,drink lots of water,take Citrucel twice a day, and sit on the toilet for 30 minutes every day at the same time to have a bowel movement. I use the slow deep breathing exercises in aiding me to have a bowel movement pain free and I'm not excessively pushing hard and forcing out the bowel movement. I can't even skip one day or I can't go the next day without it being very painful to go.